First Generation Interferometers
Barry
C.
Barish
California
Institute
of
Technology
Pasadena,
CA
91125
Abstract.
The
status
and
plans
for the
first
generation long baseline suspended mass
interferometers
TAMA,
GEO,
LIGO
and
Virgo
are
presented,
as
well
as the
expected
performances.
INTRODUCTION
The
effect
of the
propagating gravitational wave
is to
deform
space
in a
quadrupolar
form.
The
characteristics
of the
deformation
are
indicated
in
Fig.
1.
0
~
o
T
<-
\
\
9
^
*
^
©
Gravitational Waves
z
FIGURE
1.
The
effect
of
gravitational waves
for one
polarization
is
shown
at the top on a
ring
of
free
particles.
The
circle alternately elongates vertically while squashing horizontally
and
vice versa with
the
frequency
of the
gravitational wave.
The
detection technique
of
interferometry
being employed
in
the new
generation
of
detectors
is
indicated
in the
lower
figure.
The
interferometer measures
the
difference
in
distance
in two
perpendicular directions, which
if
sensitive
enough could detect
the
passage
of a
gravitational wave
For an
astrophysical source,
one can
estimate
the
frequency
of the
emitted
gravitational wave.
An
upper limit
on the
gravitational wave source
frequency
can be
estimated
from
the
Schwarzshild radius
2GM/C
2
of the
radiated object.
We do not
CP575,
Astrophysical Sources
for
Ground-Based Gravitational
Wave
Detectors,
edited
by J. M.
Centrella
©
2001
American Institute
of
Physics
0-7354-0014-8/01/$18.00
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
expect
strong
emission
for
periods
shorter
than
the
light
travel
time
4rcGM/c
3
around
its
circumference.
From
this
we can
estimate
the
maximum
frequency
as
about
10
4
Hz
for
a
solar
mass
object.
Of
course,
the
frequency
can be
much
lower
as
illustrated
by
the
8
hour
period
of
PSR1916+13,
which
is
emitting
gravitational
radiation.
Frequencies
in the
higher
frequency
range
IHz
<f<
10
4
Hz
are
potentially
reachable
using
detectors
on the
earth's
surface,
while
the
lower
frequencies
require
putting
an
instrument
into
space.
The
physics
goals
of the
terrestrial
detectors
and the
LISA
space
mission
are
complementary,
much
like
different
frequency
bands
are
used
in
observational
astronomy
for
electromagnetic
radiation
The
strength
of a
gravitational
wave
signal
depends
crucially
on the
quadrupole
moment
of the
source.
We can
roughly
estimate
how
large
the
effect
could
be
from
astrophysical
sources.
If we
denote
the
quadrupole
moment
of the
mass
distribution
of
a
source
by Q, a
dimensional
argument,
along
with
the
assumption
that
gravitational
radiation
couples
to the
quadrupole
moment
yields:
c
r c r
where
G is the
gravitational
constant
and
£™*-*
w/
"
i
s
the
non-symmetrical
part
of the
kinetic
energy.
For the
purpose
of
estimation,
let us
consider
the
case
where
one
solar
mass
is in
the
form
of
non-symmetric
kinetic
energy.
Then,
at a
distance
of the
Virgo
cluster
we
estimate
a
strain
of
h
~
10~
21
.
This
is a
good
guide
to the
largest
signals
that
might
be
observed.
At
larger
distances
or for
sources
with
a
smaller
quadrupole
component
the
signal
will
be
weaker
LONG
BASELINE
INTERFEROMETRY
A
Michelson
interferometer
operating
between
freely
suspended
masses
is
ideally
suited
to
detect
the
antisymmetric
(compression
along
one
dimension
and
expansion
along
an
orthogonal
one)
distortions
of
space
induced
by the
gravitational
waves
as
was
illustrated
in
figure
1.
Other
optical
configurations
or
interferometer
schemes,
like
a
Sagnac,
might
also
be
used
and
could
have
advantages,
but the
present
generation
of
interferometers
discussed
here
are of the
Michelson
type.
The
simplest
configuration,
a
white
light
(equal
arm)
Michelson
interferometer
is
instructive
in
visualizing
many
of the
concepts.
In
such
a
system
the two
interferometer
arms
are
identical
in
length
and in the
light
storage
time.
Light
brought
to
the
beam
splitter
is
divided
evenly
between
the two
arms
of the
interferometer.
The
light
is
transmitted
through
the
splitter
to
reach
one arm and
reflected
by the
splitter
to
reach
the
other
arm.
The
light
traverses
the
arms
and is
returned
to the
splitter
by the
distant
arm
mirrors.
The
roles
of
reflection
and
transmission
are
interchanged
on
this
return
and,
furthermore,
due to the
Fresnel
laws
of E & M the
return
reflection
is
accompanied
by a
sign
reversal
of the
optical
electric
field.
When
the
optical
electric
fields
that
have
come
from
the two
arms
are
recombined
at the
beam
splitter,
the
beams
that
were
treated
to a
reflection
(transmission)
followed
by a
transmission
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
(reflection)
emerge
at the
antisymmetric
port
of the
beam
splitter
while
those
that
have
been
treated
to
successive
reflections
(transmissions)
will
emerge
at the
symmetric
port.
In
a
simple
Michelson
configuration
the
detector
is
placed
at the
antisymmetric
port
and the
light
source
at the
symmetric
port.
If the
beam
geometry
is
such
as to
have
a
single
phase
over
the
propagating
wavefront
(an
idealized
uniphase
plane
wave
has
this
property
as
does
the
Gaussian
wavefront
in the
lowest
order
spatial
mode
of a
laser),
then,
providing
the
arms
are
equal
in
length
(or
their
difference
in
length
is a
multiple
of 1/2 the
light
wavelength),
the
entire
field
at the
antisymmetric
port
will
be
dark.
The
destructive
interference
over
the
entire
beam
wavefront
is
complete
and all
the
light
will
constructively
recombine
at the
symmetric
port.
The
interferometer
acts
like
a
light
valve
sending
light
to the
antisymmetric
or
symmetric
port
depending
on
the
path
length
difference
in the
arms.
If the
system
is
balanced
so
that
no
light
appears
at the
antisymmetric
port,
the
gravitational
wave
passing
though
the
interferometer
will
disturb
the
balance
and
cause
light
to
fall
on the
photodetector
at the
dark
port.
This
is the
basis
of the
detection
of
gravitational
waves
in a
suspended
mass
interferometer.
In
order
to
obtain
the
required
sensitivity,
the
arms
of the
interferometer
must
be
long.
x>
line
interferometer
Fabry
Perot
interferometer
FIGURE
2.
Folded
optical
configurations
for
interferometer.
The
arrangement
on the
left
is
called
a
delay
line
interferometer
and the one on the
right
using
a
resonant
cavity
is a
Fabry
Perot
interferometer.
The
GEO600
interferometer
is a
delay
line
interferometer,
while
the all the
other
long
baseline
interferometers
use
Fabry
Perot
resonant
cavities.
The
amount
of
motion
of the
arms
to
produce
an
intensity
change
at the
photodetector
depends
on the
optical
length
of the
arm;
the
longer
the arm the
greater
is
the
change
in
length
up to a
length
that
is
equal
to
1/2
the
gravitational
wave
wave-
length.
Equivalently
the
longer
the
interaction
of the
light
with
the
gravitational
wave,
up
to 1/2 the
period
of the
gravitational
wave,
the
larger
is the
optical
phase
shift
due
to the
gravitational
wave
and
thereby
the
larger
is the
intensity
change
at the
photodetector.
The
initial
long
baseline
interferometers,
besides
having
long
arms
also
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
will
fold
the
optical
beams
in the
arms
in
optical
cavities
or
delay
lines
to
gain
further
increase
in the
path
length
or
equivalently
in the
interaction
time
of the
light
with
the
gravitational
wave
(Fig.
2). The
initial
LIGO
interferometers
will
store
the
light
about
50
times
longer
than
the
beam
transit
time
in an
arm.
(A
light
storage
time
of
about
1
millisecond.)
Another
feature
employed
in
these
interferometers
is to
increase
the
change
in
intensity
due to a
phase
change
at the
antisymmetric
port
by
making
the
entire
interferometer
into
a
resonant
optical
storage
cavity.
The
fact
that
the
interferometer
is
operated
with
no
light
emerging
at the
antisymmetric
port
and all the
light
that
is not
lost
in the
mirrors
or
scattered
out of the
beam
returns
toward
the
light
source
via the
symmetric
port,
makes
it
possible
to
gain
a
significant
factor
by
placing
another
mirror
between
the
laser
and the
symmetric
port
and
'reuse
the
light'.
This
technique
is
general
referred
to as
power
recycling.
By
choosing
this
mirror's
position
properly
and
by
making
the
transmission
of
this
mirror
equal
to the
optical
losses
inside
the
interferometer,
one can
"match"
the
losses
in the
interferometer
to the
laser
so
that
no
light
is
reflected
back
to the
laser.
As a
consequence,
the
light
circulating
in the
interferometer
is
increased
by the
reciprocal
of the
losses
in the
interferometer.
This
is
equivalent
to
increasing
the
laser
power
and
does
not
affect
the
frequency
response
of
the
interferometer
to a
gravitational
wave.
The
power
gain
achieved
by
this
scheme
can be a
factor
of 10 or
even
100.
Fabry-Peiot
cavities
MieWsort
Recycling
dark
port
(GW
signal)
FIGURE
3.
The
optical
configuration
of a
Michelson
interferometer
with
Fabry-Perot
arms
is
shown.
A
relative
change
in
length
of the two
arms
causes
a
phase
shift
destroying
the
destructive
interference
and
the
dark
port
detects
a
signal
The
system
just
described
is
called
a
power
recycled
Fabry-Perot
Michelson
interferometer
and it is
this
type
of
configuration
that
will
be
used
in the
initial
interferometers
(Fig.
3).
There
are
many
other
possible
types
of
interferometer
configurations,
such
as
narrow
band
interferometers
with
the
advantage
of
increased
sensitivity
in a
narrow
frequency
range.
This
can be
accomplished
by
adding
yet
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
another
mirror
in the
output
port
and is
generally
called
signal
recycling.
Such
interferometers
are
planned
for
future
versions
of the
various
interferometers
facilities
and
the
GEO600
interferometer
has
already
incorporated
this
capability.
The
interferometer
parameters
of the new set of
detectors
just
being
brought
online
have
been
chosen
such
that
the
initial
sensitivity
will
be
consistent
both
with
the
dimensional
arguments
given
above
and
with
estimates
needed
for
possible
detection
of
known
sources.
Although
the
rate
for
these
sources
are
very
uncertain,
large
increases
in
sensitivity
are
anticipated
as the
detectors
are
improved.
This
is
because
the
planned
incremental
improvements
in
sensitivity
correspond
to the
cube
of
that
improvement
in the
event
rate,
which
scales
as the
volume
searched.
THE
INTERFEROMETER
NOISE
FLOOR
The
success
of the
detector
ultimately
will
depend
on how
well
we one can to
control
the
noise
in the
measurement
of
these
small
strains.
Noise
is
broadly
but
also
usefully
categorized
in
terms
of
those
phenomena
which
limit
the
ability
to
sense
and
register
the
small
motions
(sensing
noise
limits)
and
those
that
perturb
the
masses
by
causing
small
motions
(random
force
noise).
Eventually
one
reaches
the
ultimate
limiting
noise,
the
quantum
limit,
which
combines
the
sensing
noise
with
a
random
force
limit.
This
orderly
and
intellectually
satisfying
categorization
presumes
that
one
is
careful
enough
as
experimenters
in the
execution
of the
experiment
that
one has not
produced
less
fundamental,
albeit,
real
noise
sources
that
are
caused
by
faulty
design
or
poor
implementation.
These
might
be
referred
to as
technical
noise
sources
and in
real
life
these
have
often
been
the
impediments
to
progress
and
mask
the
limiting
noise
sources
of the
interferometer.
The
primary
noise
sources
for the
initial
detectors
are
illustrated
in
Fig.
4,
where
the
estimated
levels
of the
various
noise
sources
are
shown
for
LIGO.
The
other
interferometers
have
similar
curves
with
some
difference
in
detail
due to the
different
trade-offs
that
have
been
made.
In
order
to
control
the
technical
noise
sources,
extensive
use is
made
of two
concepts.
The
first
is the
technique
of
modulating
the
signal
to be
detected
at
frequencies
far
above
the
1/f
noise
due to the
drift
and
gain
instabilities
experienced
in
all
instruments.
For
example,
the
optical
phase
measurement
to
determine
the
motion
of the
fringe
is
carried
out at
radio
frequency
rather
than
near
DC.
Thereby,
the low
frequency
amplitude
noise
in the
laser
light
will
not
directly
perturb
the
measurement
of
the
fringe
position.
(The
low
frequency
noise
still
will
cause
radiation
pressure
fluctuations
on the
mirrors
through
the
asymmetries
in the
interferometer
arms.)
A
second
concept
is to
apply
feedback
to
physical
variables
in the
experiment
to
control
the
large
excursions
at low
frequencies
and to
provide
damping.
The
variable
is
measured
through
the
control
signal
required
to
hold
it
stationary.
Here
a
good
example
is the
position
of the
interferometer
mirrors
at low
frequency.
The
interferometer
fringe
is
maintained
at a
fixed
phase
by
holding
the
mirrors
at
fixed
positions
at low
frequencies.
Feedback
forces
to the
mirrors
effectively
hold
the
mirrors
"rigidly".
In the
initial
LIGO
interferometers
the
forces
are
provided
by
permanent
magnet/coil
combinations.
The
mirror
motion
that
would
have
occurred
is
then
read
in the
control
signal
required
to
hold
the
mirror.
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp